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A Bayesian control chart for a common coefficient of variation

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  • R. van Zyl
  • A. J. van der Merwe

Abstract

By using the medical data analyzed by Kang et al. (2007), a Bayesian procedure is applied to obtain control limits for the coefficient of variation. Reference and probability matching priors are derived for a common coefficient of variation across the range of sample values. By simulating the posterior predictive density function of a future coefficient of variation, it is shown that the control limits are effectively identical to those obtained by Kang et al. (2007) for the specific dataset they used. This article illustrates the flexibility and unique features of the Bayesian simulation method for obtaining posterior distributions, predictive intervals, and run-lengths in the case of the coefficient of variation. A simulation study shows that the 95% Bayesian confidence intervals for the coefficient of variation have the correct frequentist coverage.

Suggested Citation

  • R. van Zyl & A. J. van der Merwe, 2017. "A Bayesian control chart for a common coefficient of variation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5795-5811, June.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:12:p:5795-5811
    DOI: 10.1080/03610926.2015.1112914
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